i1 : M = random(ZZ^3, ZZ^5) o1 = | 6 0 1 0 2 | | 4 9 4 2 1 | | 2 6 7 6 4 | 3 5 o1 : Matrix ZZ <--- ZZ |
i2 : R = QQ[x,y,z] o2 = R o2 : PolynomialRing |
i3 : (Q,inG,G) = points(M,R) 2 2 2 3 2 o3 = ({1, z, y, x, z }, ideal (y*z, x*z, y , x*y, x , z ), {y*z + 3z - 6x - ------------------------------------------------------------------------ 2 2 2 6y - 37z + 114, x*z + 3z - 10x - 36z + 108, y + 4z - 3x - 11y - 39z + ------------------------------------------------------------------------ 2 2 2 3 2 108, x*y - 3z + 2x + 33z - 90, x - 5z + 6x + 58z - 168, z - 9z - ------------------------------------------------------------------------ 12x + 2z + 96}) o3 : Sequence |
i4 : monomialIdeal G == inG o4 = true |
i5 : R = ZZ/32003[vars(0..4), MonomialOrder=>Lex] o5 = R o5 : PolynomialRing |
i6 : M = random(ZZ^5, ZZ^150) o6 = | 3 8 0 7 2 6 9 6 2 3 9 5 6 2 4 6 3 3 5 3 6 7 9 3 5 1 7 4 7 3 6 4 7 5 0 | 5 0 4 7 0 3 5 3 5 5 5 2 2 1 8 3 0 9 5 2 9 8 9 1 9 2 0 1 9 6 9 7 5 7 5 | 3 2 4 9 6 9 6 4 3 1 2 6 7 1 7 8 4 9 7 9 5 0 0 1 1 3 4 3 0 0 8 5 6 3 8 | 9 8 9 7 1 6 0 0 0 2 3 1 3 6 7 7 9 2 8 6 5 3 9 9 7 6 0 6 4 2 7 0 7 2 0 | 0 3 3 9 3 1 6 2 8 4 6 7 8 1 8 7 2 3 3 5 2 9 6 6 4 2 7 5 4 1 7 0 7 8 8 ------------------------------------------------------------------------ 2 3 4 6 2 4 5 2 8 9 6 2 3 0 5 9 3 3 4 1 0 0 7 9 7 2 2 6 9 1 3 5 2 0 4 3 9 5 0 5 0 0 9 8 9 5 4 6 9 0 0 8 6 8 5 2 4 6 4 0 9 1 6 7 9 6 9 6 7 3 7 0 8 9 0 3 2 6 4 4 7 5 0 0 1 7 4 9 3 6 8 7 7 5 4 4 5 5 9 6 2 8 3 7 5 4 0 6 2 1 2 0 2 2 0 9 0 7 5 6 4 0 1 7 2 6 7 8 2 5 5 1 9 7 7 5 9 2 5 3 1 1 3 7 0 5 5 8 2 8 6 4 3 5 7 3 7 6 3 3 7 5 4 4 5 3 9 0 9 7 8 0 9 2 9 4 5 6 0 2 ------------------------------------------------------------------------ 1 5 2 7 9 3 1 9 9 6 5 8 0 9 6 1 3 8 0 4 4 5 4 8 9 2 1 1 5 2 6 6 3 4 9 5 6 0 4 8 1 0 4 9 6 4 8 2 2 6 0 7 8 2 6 5 2 8 7 2 0 7 2 4 4 2 4 4 9 3 8 0 5 0 1 0 2 4 3 9 1 4 0 3 1 2 4 6 0 3 8 9 6 4 1 5 3 3 9 2 6 1 6 2 2 1 3 0 6 7 4 6 2 4 9 4 6 2 6 5 9 4 6 5 4 8 6 3 3 6 6 5 7 9 6 7 4 1 0 3 6 3 5 8 8 5 4 9 3 8 2 9 1 8 5 6 4 8 5 0 0 7 9 6 0 7 4 6 3 9 9 7 2 8 1 1 8 6 2 6 ------------------------------------------------------------------------ 1 9 2 3 8 3 4 1 1 3 7 9 4 4 8 6 1 9 0 9 5 7 2 9 0 3 8 1 0 9 8 6 8 4 8 0 1 3 6 6 9 4 5 6 9 0 5 9 1 6 9 5 2 0 8 2 8 5 2 4 2 0 8 8 9 5 4 2 2 5 4 8 2 4 8 0 5 4 1 2 0 7 7 3 4 2 3 5 5 4 6 5 0 1 4 6 1 2 9 9 2 5 8 6 3 6 2 4 0 4 0 8 6 8 8 0 8 3 8 3 7 0 9 2 7 0 6 5 0 2 5 8 7 3 0 4 4 6 8 9 7 9 3 2 2 1 3 9 8 2 5 1 1 2 3 5 5 3 5 3 3 3 8 9 0 0 1 3 0 6 8 7 2 1 8 5 0 9 7 0 ------------------------------------------------------------------------ 6 4 4 9 7 8 5 | 8 8 7 7 5 7 3 | 5 0 9 8 8 2 9 | 8 8 4 7 7 2 6 | 3 7 3 4 4 1 5 | 5 150 o6 : Matrix ZZ <--- ZZ |
i7 : time J = pointsByIntersection(M,R); -- used 11.7312 seconds |
i8 : time C = points(M,R); -- used 0.99161 seconds |
i9 : J == C_2 o9 = true |